Why is it I can move an animated model after importing but not later?
A complex animated character consists of two parts, a mesh object and a rig that deforms it. When you move one of these paired objects in object mode the armature deformation goes bad, you need to move both objects together. Usually the armature is made the parent of the object, so moving the armature keeps it all together but moving the mesh object will be an issue.

In 2.7x while an armature is in pose mode, we can select an object and the armature will be deselected. In 2.80 this changes, while in pose mode we are unable to select another object. The solution is to go into object mode to select another object. This is also true for other modes, we need to be in object mode to select a different object.